Scheduling independent tasks on uniform processors
SIAM Journal on Computing
Tighter bounds for LPT scheduling on uniform processors
SIAM Journal on Computing
An On-Line Algorithm for Some Uniform Processor Scheduling
SIAM Journal on Computing
Exact and Approximate Algorithms for Scheduling Nonidentical Processors
Journal of the ACM (JACM)
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Truthful Mechanisms for One-Parameter Agents
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
Fast monotone 3-approximation algorithm for scheduling related machines
ESA'05 Proceedings of the 13th annual European conference on Algorithms
The Price of Anarchy on Uniformly Related Machines Revisited
SAGT '08 Proceedings of the 1st International Symposium on Algorithmic Game Theory
On designing truthful mechanisms for online scheduling
Theoretical Computer Science
Truthful Approximation Schemes for Single-Parameter Agents
SIAM Journal on Computing
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Q||Cmax denotes the problem of scheduling n jobs on m machines of different speeds such that the makespan is minimized. In the paper two special cases of Q||Cmax are considered: Case I, when m–1 machine speeds are equal, and there is only one faster machine; and Case II, when machine speeds are all powers of 2. Case I has been widely studied in the literature, while Case II is significant in an approach to design so called monotone algorithms for the scheduling problem. We deal with the worst case approximation ratio of the classic list scheduling algorithm 'Longest Processing Time (LPT)'. We provide an analysis of this ratio Lpt/Opt for both special cases: For one fast machine, a tight bound of $(\sqrt{3}+1)/2\approx 1.366$ is given. When machine speeds are powers of 2 (2-divisible machines), we show that in the worst case 41/30 Lpt/Opt To our knowledge, the best previous lower bound for both problems was 4/3–ε, whereas the best known upper bounds were 3/2–1/2m for Case I [6] resp. 3/2 for Case II [10]. For both the lower and the upper bound, the analysis of Case II is a refined version of that of Case I.